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Fierce battles between Yemeni factions in Arhab, about 15 miles from the capital, have badly damaged houses, forcing Hakma Abdallah and her children to live in a cave in a nearby hill.

ARHAB, Yemen - In this rugged northern valley ringed by pink-hued mountains, an ongoing conflict between Yemeni factions is siphoning away resources from a more significant war against Al Qaeda-linked militants in Yemen’s restive south.

And Hakma Abdallah and her 10 children are among its numerous victims. Home is a dark cave in the craggy hillside above their village. They sleep on dusty blankets on the hard earth, sharing the meager space with two other families. The houses below have been shattered by artillery shells and mortar rounds, testament to the fierce battles that have erupted here.

“The children are too afraid to sleep in our house,’’ said Abdallah, whose home was badly damaged. “The shelling can start at any moment.’’

Even as the Obama administration steps up its efforts to weaken Al Qaeda’s Yemeni branch, this Middle Eastern nation’s new US-backed president is facing a struggle for his own future. The contest for influence is playing out between loyalists of former president Ali Abdullah Saleh and his longtime opponents, most prominently in the capital, Sana, and in Arhab, on its outskirts.

That is testing the authority of President Abed Rabbo Mansour Hadi, who was vice president under Saleh, and his ability to usher Yemen into a new era after 33 years of authoritarian rule. For now, Hadi’s biggest challenge is reforming Yemen’s fractured armed forces.

But while he has had some successes, the military remains divided, beholden more to commanders who are pro- or anti-Saleh than to Hadi, who assumed office in February.

What is unfolding in Arhab, about 15 miles north of the capital, is an extension of a yearlong military standoff, fueled by fissures in the armed forces that have divided Sana and paralyzed government.

The conflict is strictly about power, but its impact is being felt in the fight against Al Qaeda, said Yemeni officials, tribal leaders, and analysts. The bulk of the country’s veteran forces, including many US-trained counterterrorism troops, have been deployed in the capital and in Arhab to preserve the political clout of their leaders, rather than to the south, to battle the militants.

Al Qaeda’s Yemeni branch has repeatedly targeted the United States, the latest attempt last month when Saudi operatives foiled a plot to bomb a US-bound jet. In recent weeks, the Obama administration has escalated its campaign of drone strikes and sent small groups of military trainers and advisers to assist Yemen’s military, including some who entered Yemen earlier this month.

But so far the ground war, although it has intensified recently, has been unable to break the Islamists, who have gained territory and resolve over the past year.

“The tensions around Sana have taken resources from the war against the terrorists in the south,’’ said Abdul Ghani al-Iriyani, a well-known political analyst.

On one side of Arhab’s conflict are tribesmen linked to Islah, the country’s most powerful Islamist party, and Ali Muhsin al-Ahmar, a renegade general. On the other side are Republican Guard troops led by Saleh’s son, Ahmed Ali Saleh.

“They are pawns in the competition between the two factions of the regime,’’ Iriyani said.

Arhab is strategically important because it is near the capital’s international airport and because it houses the most significant Republican Guard bases in the region. It is also the ancestral home of Abdul Majid al-Zindani, Yemen’s most influential cleric, whom the United States has labeled a terrorist for his reputed links to Al Qaeda.

The conflict in Arhab began last summer, after Muhsin and his First Armored Brigade joined Yemen’s prodemocracy uprising, and after government troops killed dozens of protesters in Sana and in the south-central city of Taiz. Zindani, who like Muhsin is a senior Islah leader, also sided with the protesters.

The tribesmen of Arhab also backed the protesters, rising to prevent the Republican Guards from entering the capital and quashing the revolution. They launched attacks on their mountain bases, firing rockets and mortars. The Republican Guards responded by pounding the valley with shells and aerial strikes. Thousands fled their homes, many seeking shelter in the caves, with no water or electricity and very little food.

The fighting raged on, even after a power transfer deal brokered by Yemen’s Gulf neighbors and the United States paved the way for Saleh to step down in November.

Hadi, who was Saleh’s hand-picked successor, has surprised his critics by ousting Saleh’s half brother and a nephew from key positions in the military. However, he has not tried to dismiss Ahmed Ali Saleh or his other cousins, who command powerful sections of the military.

For the tribesmen in Arhab, the Republican Guards are the most visible symbol of the old order. People in the valley refer to the forces as “the Family Guards.’’

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